Find Where Undefined/Discontinuous 2/x=1/(2x)+3

$\frac{2}{x} = \frac{1}{2 x} + 3$

Step 1

Move all the expressions to the left side of the equation.

Subtract $\frac{1}{2 x}$ from both sides of the equation.

$\frac{2}{x} - \frac{1}{2 x} = 3$

Subtract $3$ from both sides of the equation.

$\frac{2}{x} - \frac{1}{2 x} - 3 = 0$

Step 2

Simplify $\frac{2}{x} - \frac{1}{2 x} - 3$ .

To write $\frac{2}{x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2}{x} \cdot \frac{2}{2} - \frac{1}{2 x} - 3 = 0$

Write each expression with a common denominator of $x \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{x}$ by $\frac{2}{2}$ .

$\frac{2 \cdot 2}{x \cdot 2} - \frac{1}{2 x} - 3 = 0$

Move $2$ to the left of $x$ .

$\frac{2 \cdot 2}{2 x} - \frac{1}{2 x} - 3 = 0$

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 - 1}{2 x} - 3 = 0$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 - 1}{2 x} - 3 = 0$

Subtract $1$ from $4$ .

$\frac{3}{2 x} - 3 = 0$

Step 3

Set the denominator in $\frac{3}{2 x}$ equal to $0$ to find where the expression is undefined.

$2 x = 0$

Step 4

Divide each term in $2 x = 0$ by $2$ and simplify.

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x = 0$

Step 5